Bounds on the Expected Size of the Maximum Agreement Subtree

We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question posed in earlier work. Determining tight upper and lower bounds remains an open problem.Comment: Revised versio

Categorification of a linear algebra identity and factorization of Serre functors

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre functor of a finite dimensional triangular algebra A has always a lift, up to shift, to a product of suitably defined reflection functors in the category of perfect complexes over the trivial extension algebra of A.Comment: 18 pages; Minor changes, references added, new Section 2.

Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Profilin modulates sarcomeric organization and mediates cardiomyocyte hypertrophy

Aims: Heart failure is often preceded by cardiac hypertrophy, which is characterized by increased cell size, altered protein abundance, and actin-cytoskeletal reorganization. Profilin is a well-conserved, ubiquitously expressed, multi-functional actin-binding protein, whose role in cardiomyocytes is largely unknown. Given its involvement in vascular hypertrophy, we aimed to test the hypothesis that profilin-1 is a key mediator of cardiomyocyte-specific hypertrophic remodeling. Methods and Results: Profilin-1 was elevated in multiple mouse models of hypertrophy, and a cardiomyocyte-specific increase of profilin in Drosophila resulted in significantly larger heart tube dimensions. Moreover, adenovirus-mediated overexpression of profilin-1 in neonatal rat ventricular myocytes (NRVMs) induced a hypertrophic response, measured by increased myocyte size and gene expression. Profilin-1 silencing suppressed the response in NRVMs stimulated with phenylephrine or endothelin-1. Mechanistically, we found that profilin-1 regulates hypertrophy, in part, through activation of the ERK1/2 signaling cascade. Confocal microscopy showed that profilin localized to the Z-line of Drosophila myofibrils under normal conditions and accumulated near the M-line when overexpressed. Elevated profilin levels resulted in elongated sarcomeres, myofibrillar disorganization, and sarcomeric disarray, which correlated with impaired muscle function. Conclusion: Our results identify novel roles for profilin as an important mediator of cardiomyocyte hypertrophy. We show that overexpression of profilin is sufficient to induce cardiomyocyte hypertrophy and sarcomeric remodeling, and silencing of profilin attenuates the hypertrophic response

Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Regulation of the Cardiac Na+/K+ ATPase by Phospholemman

Hansraj Dhayan, Rajender Kumar, Andreas Kukol, ‘Regulation of the Cardiac Na+/K+ ATPase by Phospholemman’, in Sajal Chakraborti, Naranjan Dhalla, eds., Regulation of Membrane Na+-K+ ATPase, (Switzerland: Springer, 2016), ISBN 978-3-319-24748-9, eISBN 978-3-319-24750-2.Peer reviewe

Comparative genomic analysis of the arthropod muscle myosin heavy chain genes allows ancestral gene reconstruction and reveals a new type of 'partially' processed pseudogene

<p>Abstract</p> <p>Background</p> <p>Alternative splicing of mutually exclusive exons is an important mechanism for increasing protein diversity in eukaryotes. The insect <it>Mhc </it>(myosin heavy chain) gene produces all different muscle myosins as a result of alternative splicing in contrast to most other organisms of the Metazoa lineage, that have a family of muscle genes with each gene coding for a protein specialized for a functional niche.</p> <p>Results</p> <p>The muscle myosin heavy chain genes of 22 species of the Arthropoda ranging from the waterflea to wasp and <it>Drosophila </it>have been annotated. The analysis of the gene structures allowed the reconstruction of an ancient muscle myosin heavy chain gene and showed that during evolution of the arthropods introns have mainly been lost in these genes although intron gain might have happened in a few cases. Surprisingly, the genome of <it>Aedes aegypti </it>contains another and that of <it>Culex pipiens quinquefasciatus </it>two further muscle myosin heavy chain genes, called <it>Mhc3 </it>and <it>Mhc4</it>, that contain only one variant of the corresponding alternative exons of the <it>Mhc1 </it>gene. <it>Mhc3 </it>transcription in <it>Aedes aegypti </it>is documented by EST data. <it>Mhc3 </it>and <it>Mhc4 </it>inserted in the <it>Aedes </it>and <it>Culex </it>genomes either by gene duplication followed by the loss of all but one variant of the alternative exons, or by incorporation of a transcript of which all other variants have been spliced out retaining the exon-intron structure. The second and more likely possibility represents a new type of a 'partially' processed pseudogene.</p> <p>Conclusion</p> <p>Based on the comparative genomic analysis of the alternatively spliced arthropod muscle myosin heavy chain genes we propose that the splicing process operates sequentially on the transcript. The process consists of the splicing of the mutually exclusive exons until one exon out of the cluster remains while retaining surrounding intronic sequence. In a second step splicing of introns takes place. A related mechanism could be responsible for the splicing of other genes containing mutually exclusive exons.</p

Sarcomere Formation Occurs by the Assembly of Multiple Latent Protein Complexes

The stereotyped striation of myofibrils is a conserved feature of muscle organization that is critical to its function. Although most components that constitute the basic myofibrils are well-characterized biochemically and are conserved across the animal kingdom, the mechanisms leading to the precise assembly of sarcomeres, the basic units of myofibrils, are poorly understood. To gain insights into this process, we investigated the functional relationships of sarcomeric protein complexes. Specifically, we systematically analyzed, using either RNAi in primary muscle cells or available genetic mutations, the organization of myofibrils in Drosophila muscles that lack one or more sarcomeric proteins. Our study reveals that the thin and thick filaments are mutually dependent on each other for striation. Further, the tension sensor complex comprised of zipper/Zasp/α-actinin is involved in stabilizing the sarcomere but not in its initial formation. Finally, integrins appear essential for the interdigitation of thin and thick filaments that occurs prior to striation. Thus, sarcomere formation occurs by the coordinated assembly of multiple latent protein complexes, as opposed to sequential assembly

Identification of preferential target sites for human DNA methyltransferases

DNA methyltransferases (DNMTs) play an important role in establishing and maintaining DNA methylation. Aberrant expression of DNMTs and their isoforms has been found in many types of cancer, and their contribution to aberrant DNA methylation has been proposed. Here, we generated HEK 293T cells stably transfected with each of 13 different DNMTs (DNMT1, two DNMT3A isoforms, nine DNMT3B isoforms and DNMT3L) and assessed the DNA methylation changes induced by each DNMT. We obtained DNA methylation profiles of DNA repetitive elements and 1505 CpG sites from 808 cancer-related genes. We found that DNMTs have specific and overlapping target sites and their DNA methylation target profiles are a reflection of the DNMT domains. By examining H3K4me3 and H3K27me3 modifications in the 808 gene promoter regions using promoter ChIP-on-chip analysis, we found that specific de novo DNA methylation target sites of DNMT3A1 are associated with H3K4me3 modification that are transcriptionally active, whereas the specific target sites of DNMT3B1 are associated with H3K27me3 modification that are transcriptionally inactive. Our data suggest that different DNMT domains are responsible for targeting DNA methylation to specific regions of the genome, and this targeting might be associated with histone modifications

Study protocol to investigate the effect of a lifestyle intervention on body weight, psychological health status and risk factors associated with disease recurrence in women recovering from breast cancer treatment

Background Breast cancer survivors often encounter physiological and psychological problems related to their diagnosis and treatment that can influence long-term prognosis. The aim of this research is to investigate the effects of a lifestyle intervention on body weight and psychological well-being in women recovering from breast cancer treatment, and to determine the relationship between changes in these variables and biomarkers associated with disease recurrence and survival. Methods/design Following ethical approval, a total of 100 patients will be randomly assigned to a lifestyle intervention (incorporating dietary energy restriction in conjunction with aerobic exercise training) or normal care control group. Patients randomised to the dietary and exercise intervention will be given individualised healthy eating dietary advice and written information and attend moderate intensity aerobic exercise sessions on three to five days per week for a period of 24 weeks. The aim of this strategy is to induce a steady weight loss of up to 0.5 Kg each week. In addition, the overall quality of the diet will be examined with a view to (i) reducing the dietary intake of fat to ~25% of the total calories, (ii) eating at least 5 portions of fruit and vegetables a day, (iii) increasing the intake of fibre and reducing refined carbohydrates, and (iv) taking moderate amounts of alcohol. Outcome measures will include body weight and body composition, psychological health status (stress and depression), cardiorespiratory fitness and quality of life. In addition, biomarkers associated with disease recurrence, including stress hormones, estrogen status, inflammatory markers and indices of innate and adaptive immune function will be monitored. Discussion This research will provide valuable information on the effectiveness of a practical, easily implemented lifestyle intervention for evoking positive effects on body weight and psychological well-being, two important factors that can influence long-term prognosis in breast cancer survivors. However, the added value of the study is that it will also evaluate the effects of the lifestyle intervention on a range of biomarkers associated with disease recurrence and survival. Considered together, the results should improve our understanding of the potential role that lifestyle-modifiable factors could play in saving or prolonging lives